214 GENETICS: J. A. HARRIS ET AL. PROC. N. A. S 



In a population the straight line relating the egg production of a period 

 K/&amp;gt; with that of a period used as a basis of prediction, e, is 



where the bars denote means, the sigmas represent standard deviations, 

 and r indicates the correlation of the two variables in the standard popu 

 lation. 



The value of Ep given by the equation is the theoretical mean produc 

 tion for the array of individuals of any class with respect to e. The as 

 sumption to be tested is that we may write E p and e instead of E p and 

 e, where E/ is the theoretical mean production for a period p of the array 

 of birds of any grade of production e in the period used as a basis of pre 

 diction in a series of birds which are not involved in the data upon which 

 the equations were based, but to which the equations are to be applied for 

 practical purposes. 



The essential practical requisites for such prediction equations are: (1) 

 That the errors of prediction shall be distributed about the true numbers 

 in such a manner that estimation will not in the long run be either too 

 high or too low. (2) That the magnitude of the deviation of the predicted 

 from the observed egg production shall be as small as possible. 



Let Ep&quot; be the actual and E P the predicted egg production of an in 

 dividual bird for any period, p, in a flock to which the equation is being 

 applied. The error of prediction is then E P E P .&quot; The average of these 

 errors, with regard to sign 



N* 



furnishes a measure of the success with which the first requirement, (1) 

 above, is met. The average of these errors without regard to sign fur 

 nishes a measure of the average error above or below the true production 

 of the individual birds of a flock. The square root of mean square devia 

 tion 



furnishes a measure of this error which weights larger errors. 



The errors may be expressed in actual numbers of eggs, or, in relative 

 terms, as percentages of the mean production of the period and flock for 

 which prediction is made. Both methods have been used in testing the 

 equations. 



In testing the efficiency of such equations for purposes of predictic 

 we have proceeded in a purely objective manner. Working on the 

 sumption that the crucial test of any theory is its capacity for predict 



